OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..90
Index entries for linear recurrences with constant coefficients, signature (128405450991,-128405450991,1).
FORMULA
a(n+2) = 128405450990*a(n+1) - a(n) + 62402725494.
G.f.: x*(51721 + 64202725495*x - 51722*x^2)/((1-x)*(1 - 128405450990*x + x^2)). - Colin Barker, Oct 21 2014, corrected Jul 13 2016
EXAMPLE
a(1)=51721 because the first relation is : 51722^3 - 51721^3 = 103*8827^2.
MAPLE
seq(coeff(series(x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x + x^2)), x, n+1), x, n), n = 1..20); # G. C. Greubel, Jan 12 2020
MATHEMATICA
LinearRecurrence[{128405450991, -128405450991, 1}, {51721, 6641322533431006, 852782015075257741682069713}, 20] (* G. C. Greubel, Jan 12 2020 *)
PROG
(PARI) Vec(x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x+x^2)) + O(x^10)) \\ Colin Barker, Oct 21 2014, corrected Jul 13 2016
(PARI) isok(x) = issquare(((x+1)^3-x^3)/103) \\ Colin Barker, Jul 13 2016
(Magma) I:=[51721, 6641322533431006]; [n le 2 select I[n] else 128405450990*Self(n-1) - Self(n-2) + 62402725494: n in [1..20]]; // G. C. Greubel, Jan 12 2020
(Sage)
def A147530_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x + x^2)) ).list()
a=A147530_list(20); a[1:] # G. C. Greubel, Jan 12 2020
(GAP) a:=[51721, 6641322533431006];; for n in [3..20] do a[n]:=128405450990*a[n-1] -a[n-2] +62402725494; od; a; # G. C. Greubel, Jan 12 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Richard Choulet, Nov 06 2008
EXTENSIONS
Editing and a(6) from Colin Barker, Oct 21 2014
a(3) to a(6) corrected by Colin Barker, Jul 13 2016
STATUS
approved